When I learnt Spanish, I learnt that the translation of "to long for" is "anhelar" but I am not fluent so don't trust me too much on this.
When you "long for" someone or something, you have a deep and continuous desire for that person or thing. So if you don't see your girlfriend much and you think about her all the time, you "long for" her.
Or if you love the Hobbit films, you might be "longing to see" or "longing for" the final episode.
A common synonym for "long for" is "yearn for"